Answer:
126°
Step-by-step explanation:
Circle Theorem vocabulary
- Chord: a straight line joining two points on the circle.
- Inscribed angle: the angle formed (vertex) when two chords meet at one point on a circle.
- Arc: the curve between two points on the circumference of a circle
- Intercepted arc: the arc that is between the endpoints of the chords that form the inscribed angle.
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of the intercepted arc.
Therefore:
[tex]\displaystyle \angle RST=\dfrac{1}{2} \overset{\frown}{RT}[/tex]
[tex]\implies 63^{\circ}=\dfrac{1}{2} \overset{\frown}{RT}[/tex]
[tex]\implies \overset{\frown}{RT}= 2 \cdot 63^{\circ}[/tex]
[tex]\implies \overset{\frown}{RT}= 126^{\circ}[/tex]
